Binary, Octal, Decimal, and Hexadecimal Calculations
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1 Chapter 5 Binary, Octal, Decimal, and Hexadecimal Calculations This calculator is capable of performing the following operations involving different number systems. Number system conversion Arithmetic operations Negative values Logical operations 5-1 Before Beginning a Binary, Octal, Decimal, or Hexadecimal Calculation 5-2 Selecting a Number System 5-3 Arithmetic Operations 5-4 Negative Values and Logical Operations
2 5-1 Before Beginning a Binary, Octal, Decimal, or Hexadecimal Calculation P.5 You can use the RUN Mode and binary, octal, decimal, and hexadecimal settings to perform calculations that involve binary, octal, decimal and hexadecimal values. You can also convert between number systems and perform logical operations. You cannot use scientific functions in binary, octal, decimal, and hexadecimal calculations. You can use only integers in binary, octal, decimal, and hexadecimal calculations, so fractional values are not allowed. If you input a value that includes a decimal part, the unit automatically cuts off the decimal part. If you attempt to enter a value that is invalid in the number system (binary, octal, decimal, hexadecimal) you are using, the calculator displays an error message. The following shows the numerals that can be used in each number system. Binary: 0, 1 Octal: 0, 1, 2, 3, 4, 5, 6, 7 Decimal: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Hexadecimal: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F The alphabetic characters used in the hexadecimal number appear differently on the display to distinguish them from text characters. Normal Text: A, B, C, D, E, F Hexadecimal Values: u, v, w, x, y, z Negative binary, octal, and hexadecimal values are produced using the two s complement of the original value. The following are the display capacities for each of the number systems. Number System Binary Octal Decimal Hexadecimal Display Capacity 16 digits 11 digits 10 digits 8 digits The following are the calculation ranges for each of the number systems. Binary Values Positive: 0 < x < Negative: < x <
3 Before Beginning a Binary, Octal, Decimal, or Hexadecimal Calculation 5-1 Octal Values Positive: 0 < x < Negative: < x < Decimal Values Positive: 0 < x < Negative: < x < 1 Hexadecimal Values Positive: 0 < x < 7FFFFFFF Negative: < x < FFFFFFFF uto perform a binary, octal, decimal, or hexadecimal calculation 1. In the main menu, select RUN icon. 2. Press!Z and then specify the defalut number system by pressing 2 (Dec), 3 (Hex), 4 (Bin), or 5 (Oct). 2(Dec) 3. Press J to change to the screen for calculation input. J 1 (d~o)... Number system specification menu 2 (LOG)... Logical operation menu 87
4 5-2 Selecting a Number System You can specify decimal, hexadecimal, binary, or octal as the default number system using the set up screen. After you press the function key that corresponds to the system you want to use, press w. uto convert a displayed value from one number system to another Example To convert 2210 (default number system) to its binary or octal value A!Z2(Dec)J1(d~o)1(d) ccw!z4(bin)jw!z5(oct)jw uto specify a number system for an input value You can specify a number system for each individual value you input. While binary, octal, decimal, or hexadecimal is set as the default number system, press 1 (d~o) to display a menu of number system symbols. Press the function key that corresponds to the symbol you want to select and then input the value you want. 1(d ~ o) 1 (d)... Specifies decimal for input value 2 (h)... Specifies hexadecimal for input value 3 (b)... Specifies binary for input value 4 (o)... Specifies octal for input value uto input values of mixed number systems Example To input or 10102, when the default number system is hexadecimal!z3(hex)j A1(d~o)1(d)bcdw 3(b)babaw 88
5 5-3 Arithmetic Operations Example 1 To calculate !Z4(Bin)J Ababbb+ bbabaw Example 2 To input and execute 1238 ABC16, when the default number system is decimal or hexadecimal!z2(dec)j A1(d~o)4(o)bcd* 2(h)ABCw!Z3(Hex)Jw 89
6 5-4 Negative Values and Logical Operations While binary, octal, decimal, or hexadecimal is set as the default number system, press 2 (LOG) to display a menu of negation and logical operators. 2(LOG) 1 (Neg)... negation 2 (Not)... NOT 3 (and)... AND 4 (or)... OR 5 (xor)... XOR 6 (xnor)... XNOR k Negative Values Example To calculate the negative of !Z4(Bin)J A2(LOG)1(Neg) bbaabaw k Logical Operations Example 1 To input and execute and AD16!Z3(Hex)J Abca2(LOG) 3(and)ADw Example 2 To calculate 368 or to its octal value!z5(oct)j Adg2(LOG) 4(or)J1(d~o)3(b) bbbaw Example 3 To negate 2FFFED16!Z3(Hex)J A2(LOG)2(Not) cfffedw 90
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